Sh:726

• Shelah, S., & Väänänen, J. A. (2005). A note on extensions of infinitary logic. Arch. Math. Logic, 44(1), 63–69. arXiv: math/0009080 DOI: 10.1007/s00153-004-0212-8 MR: 2116833
• Abstract:
  We show that a strong form of the so called Lindström’s Theorem fails to generalize to extensions of L_{\kappa\omega} and L_{\kappa\kappa}: For weakly compact \kappa there is no strongest extension of L_{\kappa\omega} with the (\kappa,\kappa)-compactness property and the Löwenheim-Skolem theorem down to \kappa. With an additional set-theoretic assumption, there is no strongest extension of L_{\kappa\kappa} with the (\kappa,\kappa)-compactness property and the Löwenheim-Skolem theorem down to <\kappa.
• Version 2001-06-08_11 (10p) published version (7p)

@article{Sh:726,
 author = {Shelah, Saharon and V{\"a}{\"a}n{\"a}nen, Jouko A.},
 title = {{A note on extensions of infinitary logic}},
 journal = {Arch. Math. Logic},
 fjournal = {Archive for Mathematical Logic},
 volume = {44},
 number = {1},
 year = {2005},
 pages = {63--69},
 issn = {0933-5846},
 mrnumber = {2116833},
 mrclass = {03C75 (03C80 03C95)},
 doi = {10.1007/s00153-004-0212-8},
 note = {\href{https://arxiv.org/abs/math/0009080}{arXiv: math/0009080}},
 arxiv_number = {math/0009080}
}